Question 247: Gravitation

Question

In the reported figure of earth, the value of acceleration due to gravity is same at point A and C but it is smaller than that of its value at point B (surface of the earth). The value of OA : AB will be x : y. The value of x is ________.

Accepted Answer

$${g_A} = {{GM(r)} \over {{R^3}}}$$
$${g_C} = {{GM} \over {{{\left( {R + {R \over 2}} ight)}^2}}}$$
Given, g
A
= g
C
$$ \Rightarrow {{GM(r)} \over {{R^3}}} = {{GM} \over {{{\left( {R + {R \over 2}} ight)}^2}}}$$
$$ \Rightarrow {r \over {{R^3}}} = {4 \over {9{R^2}}}$$
$$ \Rightarrow r = {{4R} \over 9}$$
$$ 	herefore $$ $$OA = {{4R} \over 9}$$
$$ 	herefore $$ $$AB = R - r = {{5R} \over 9}$$
$$ 	herefore $$ $$OA:AB = 4:5$$
$$ 	herefore $$ x = 4

Gravitation

In the reported figure of earth, the value of acceleration due to gravity is same at point A and C but it is smaller than that of its value at point B (surface of the earth). The value of OA : AB will be x : y. The value of x is ________.

Integer / Numeric Answer Type